Invoking the predictive approach with a fixed population set-up, and employing initially the customary ratio and product estimators as potential predictors for the non-surveyed part of the population, we have generated sequences of ratio-based and product-based estimators. The proposed ratio-based and product-based estimators of order k are-under some practical conditions-found to be more efficient than the customary ratio and product estimators and the usual simple mean when k is chosen optimally. Under the optimal value of k, the kth-order ratio-based and product-based estimators are found to be as efficient as the linear regression estimator. We have used real population data to illustrate the efficacy of the proposed ratio-based and product-based estimators relative to the usual simple mean and the customary ratio and product estimators.